Halperin conjecture

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In rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician Stephen Halperin.

Contents

Statement

Suppose that is a fibration of simply connected spaces such that is rationally elliptic and (i.e., has non-zero Euler characteristic), then the Serre spectral sequence associated to the fibration collapses at the page. [1]

Status

As of 2019, Halperin's conjecture is still open. Gregory Lupton has reformulated the conjecture in terms of formality relations. [2]

Notes

  1. Berglund
  2. Lupton

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